Global dynamics of the Buckingham’s two-body problem

Jaume Llibre, Claudia Valls, Claudio Vidal

Research output: Contribution to journalArticleResearch

Abstract

© 2018, Springer Nature B.V. The equations of motion of the Buckingham system are the ones of a two-body problem defined by the Hamiltonian H=12(px2+py2)+Ae−Bx2+y2−M(x2+y2)3, where A, B and M are positive constants. The angular momentum pθ: = xpy− ypx and this Hamiltonian are two independent first integrals in involution. We denote by Ih (respectively, Ic) the set of points of the phase space where H (respectively, pθ) takes the value h (respectively, c). Due to the fact that H and pθ are first integrals, the sets Ih and Ihc= Ih∩ Ic are invariant under the flow of the Buckingham systems. We describe the global dynamics of the Buckingham system describing the foliation of its phase space by the invariant sets Ih, the foliation of the invariant set Ih by its invariant subsets Ihc, and the foliation of invariant set Ihc by the orbits of the system.
Original languageEnglish
Article number255
JournalAstrophysics and Space Science
Volume363
DOIs
Publication statusPublished - 1 Dec 2018

Keywords

  • Buckingham equations
  • Global dynamics
  • Hill regions

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